Question: Express your answer as a mixed number simplified to lowest terms. $3\dfrac{1}{3}-1\dfrac{7}{19} = {?}$
Explanation: Find a common denominator for the fractions: $= {3\dfrac{19}{57}}-{1\dfrac{21}{57}}$ Convert ${3\dfrac{19}{57}}$ to ${2 + \dfrac{57}{57} + \dfrac{19}{57}}$ So the problem becomes: ${2\dfrac{76}{57}}-{1\dfrac{21}{57}}$ Separate the whole numbers from the fractional parts: $= {2} + {\dfrac{76}{57}} - {1} - {\dfrac{21}{57}}$ Bring the whole numbers together and the fractions together: $= {2} - {1} + {\dfrac{76}{57}} - {\dfrac{21}{57}}$ Subtract the whole numbers: $=1 + {\dfrac{76}{57}} - {\dfrac{21}{57}}$ Subtract the fractions: $= 1+\dfrac{55}{57}$ Combine the whole and fractional parts into a mixed number: $= 1\dfrac{55}{57}$